Dynamical system methods have been extensively used in the context of dark energy models and modified gravity (See Ref.[1]} for a review). For \(f(R)\)  gravity the very first attempt to employ a phase space analysis can be traced back to Starobinsky [2]} in the context of \(R^2\) -inflation model. Capozziello et al. generalised this study for a number of different inflationary \(f(R)\)  models [3]}. The so called expansion-normalized dynamical variables, which are mostly used today for dynamical system analysis, was introduced for the first time by Carloni et. al. [4]} for the simple case of \(R^n\)  gravity. Attempts to generalise the formulation followed shortly afterwards [5]}, [6]}. Extensions of this formulation to a compact phase space, allowing for the analysis of asymptotic behaviour including static and cyclic solutions, were also introduced in reference to a number of \(f(R)\)  models [7]}, [8]}. Despite its success, this formulation is useful only for very certain types of \(f(R)\) . This shortcoming led Carloni to propose a different dynamical system formulation that can in principle be used for all the \(f(R)\)  theories [9]}. A form-independent dynamical system approach, that can be used for all possible \(f(R)\)  theories satisfying an observational requirement irrespective of their functional form, was proposed very recently by Chakraborty et al. [10]}.
